Final answer:
Based on the information provided, the genetic disease in question is most likely autosomal recessive because it is present in siblings, but not in Kathy, Joe, or their parents, suggesting a recessive pattern of inheritance.
Step-by-step explanation:
The fact that neither Kathy nor Joe, nor their parents have the genetic disease but a sibling of each does suggest that the disease is likely autosomal recessive. This is because autosomal recessive diseases require individuals to have two copies of the recessive gene (be homozygous recessive) to express the disease. As Kathy and Joe are healthy, it's possible that they, along with their parents, are carriers of the disease (heterozygous), meaning they possess one copy of the recessive gene but do not exhibit any symptoms because their unaffected gene compensates.
Autosomal dominant genetic diseases, on the other hand, only require one faulty gene to be expressed. Since neither Kathy nor Joe exhibits the disease, it is unlikely to be autosomal dominant; if it was, at least one of their parents would likely show symptoms because they would need to possess and pass on the dominant faulty gene.
Autosomal recessive genetic disorders include conditions like cystic fibrosis and Tay-Sachs disease. Unlike these, autosomal dominant disorders like Huntington's disease manifest with just one copy of the abnormal gene and can sometimes appear later in life.